Volatility Dynamics in Indian Equity Markets: A Comparative Study of ARCH, GARCH, and GJR-GARCH Models

This paper provides a comprehensive empirical analysis of volatility dynamics in the Indian equity market using daily log returns of the Nifty 50 index and five large-cap stocks (HDFC Bank, ICICI Bank, Infosys, Reliance, TCS) over the period 2015-2024.

We document the presence of stylized facts including extreme leptokurtosis (Nifty 50 kurtosis = 23.40), negative skewness, and volatility clustering. Three autoregressive conditional heteroskedasticity models - ARCH(1), GARCH(1,1), and GJR-GARCH(1,1,1) - are estimated and compared using AIC.

Key Findings:
- GJR-GARCH provides superior fit for ALL 6 assets (100%)
- Volatility persistence (α+β) ranges from 0.884 (Infosys) to 0.978 (ICICI Bank)
- Extreme kurtosis of 23.40 for Nifty 50 indicates massive fat tails
- Leverage effects confirmed across all assets

These findings have important implications for risk management, derivatives pricing, and portfolio construction in Indian financial markets.

Keywords: GARCH, GJR-GARCH, Volatility Modeling, Indian Equity Market, Volatility Clustering, Leverage Effect, Emerging Markets

JEL Classification: C32, C58, G11, G17